It’s easy to determine the manner in which advantage risk and you can asked get back is regarding the danger reputation of your own zero money means, the correlation into the financial support, and its Sharpe Proportion.
Replacing k inside the picture (16) gives the matchmaking ranging from step one) house chance and you may dos) the chance status and relationship of your own approach into the investment:
which ultimately shows that expected get back with the property is related yourself to your device of the chance status minutes the latest Sharpe Proportion of your strategy.
By selecting an appropriate scale, any zero investment strategy can be used to achieve a desired level (k) of relative risk. This level, plus the strategy’s Sharpe Ratio, will determine asset expected return, as shown by equation (21). Asset risk, however, will depend on both the relative risk (k) and the correlation of the strategy with the other investment (rhoId ). In general, the Sharpe Ratio, which does not take that correlation into account, will not by itself provide sufficient information to determine a set of decisions that will produce an optimal combination of asset risk and return, given an investor’s tolerance of risk.
Luckily for us, discover very important special instances where Sharpe Proportion usually provide sufficient recommendations to have behavior on the maximum risk/return combination: one out of that your pre-current portfolio are riskless, the other in which it is high-risk.
Incorporating a solution to an excellent Riskless Portfolio
Assume very first you to definitely a trader intends to spend some money between a riskless asset and you can a single risky fund (e.g.